Control system for the characteristic parameters of an active filter

ABSTRACT

A control system for the characteristic parameters of an active filter includes: a system for the determination of the technological distribution of the components that provides the information related to said technological distribution of the components; an elaboration system for said information related to said technological distribution of the components; an active filter including at least two programmable passive circuital elements receiving said information related to said technological distribution of the components; said elaboration system, being aware of the topology for said active filter, comprises means for determining the value for said at least two programmable passive circuital elements; means for correcting the value for said at least two programmable passive circuital elements according to the value of the information related to said technological distribution of the components; means for determining the programming values for said at least two programmable passive circuital elements.

PRIORITY CLAIM

[0001] This application claims priority from European patent applicationNo. 03425120.7, filed Feb. 26, 2003, which is incorporated herein byreference.

TECHNICAL FIELD

[0002] An embodiment of the present invention is directed to a controlsystem and method for controlling the characteristic parameters of anactive filter.

BACKGROUND

[0003] Active filters are normally realized with different techniquesand topologies.

[0004] A known filter solution is, for instance, that of a RC activefilter that uses a biquadratic cell with two operational amplifiers.

[0005] The characteristic parameters of a filter are the gain A0, thecutoff frequency ω0 and the quality factor Q.

[0006] Because of the technological variations of the components used(normally realized by integrated circuits) the above-mentionedparameters can vary and differ from their design nominal value. For thisreason a control system to adapt their values is often necessary.

[0007] In the specific case of a RC active filter that uses abiquadratic cell with two operational amplifiers, and also in othercases, it is possible to modify the characteristic parameters of afilter by modifying three different components.

[0008] In other cases, for instance, for filters that use only oneoperational amplifier, the value of the three above mentioned parameters(A0, ω0, Q) depends on the same components, so that by modifying aparameter the value of the other two also changes.

SUMMARY

[0009] An embodiment of the present invention provides a control systemfor the characteristic parameters of an active filter that does not havethe drawbacks of the known art.

[0010] According to an embodiment of the present invention, the controlsystem for the characteristic parameters of an active filter comprises:a system for the determination of the component technologicaldistribution that provides the information related to said componenttechnological distribution; an elaboration system for said informationrelated to said component technological distribution; an active filterincluding at least two programmable passive circuital elements receivingsaid information related to said component technological distribution;said elaboration system, being aware of the topology of said activefilter, comprises means for determining the value of said at least twoprogrammable passive circuital elements; means for correcting the valueof said at least two programmable passive circuital elements accordingto the value of the information related to said component technologicaldistribution; means for determining the programming values of said atleast two programmable passive circuital elements.

[0011] According to an other embodiment of the present invention, acontrol method for the characteristic parameters of an active filtercomprises: a system for the determination of the component technologicaldistribution that provides the information related to said componenttechnological distribution; an elaboration system for said informationrelated to said component technological distribution; an active filterincluding at least two programmable passive circuital elements receivingsaid information related to said component technological distribution;said elaboration system, being aware of the topology of said activefilter, determines the value of said at least two programmable passivecircuital elements; it corrects the value of said at least twoprogrammable passive circuital elements according to the value of theinformation related to said component technological distribution; itdetermines the programming values of said at least two programmablepassive circuital elements.

[0012] In an embodiment of the present invention it is possible torealize a control system for the characteristic parameters of an activefilter which is able to set the component values in order to get therequired characteristic parameters of a filter. That is, a system can berealized that is able to determine the component technologicaldistribution. The information so obtained will make the working of thesystem more efficient. But advance knowledge of some quantitativecharacteristics of the transfer function associated with the filter maybe needed.

DESCRIPTION OF DRAWINGS

[0013] Features and the advantages of the present invention will be mademore evident by the following detailed description of embodimentsthereof illustrated as a non-limiting example in the annexed drawings,wherein:

[0014]FIG. 1 represents an active filter with a single operationalamplifier according to an embodiment of the invention;

[0015]FIG. 2 represents a system according to an embodiment of theinvention for the determination of the component technologicaldistribution of the filter of FIG. 1;

[0016]FIG. 3 represents an embodiment of the resistance arrayillustrated in FIG. 2; and

[0017]FIG. 4 represents a block diagram of a control system for thecharacteristic parameters of an active filter according to an embodimentof the present invention.

DETAILED DESCRIPTION

[0018] In FIG. 1 a biquadratic cell 10 is represented with only oneoperational amplifier OP1. Particularly it is a low-pass filter.Embodiments of the present invention are also applicable to otherfilters either of different type (band-pass, high-pass) or of differenttopology with a single operational amplifier.

[0019] The voltage Vin is applied to the resistance R1, that isconnected to a capacitor C1 connected to ground, to a resistance R3connected to the output of the operational amplifier OP1, and to aresistance R2 connected to the inverting input of the operationalamplifier OP1. Between the inverting input of the operational amplifierOP1 and its output, a capacitor C2 is connected. The non-inverting inputof the operational amplifier OP1 is connected to ground. The output ofthe operational amplifier OP1 provides the voltage Vout.

[0020] The transfer function of the circuit of FIG. 1 is the following:$\frac{V_{out}}{V_{i\quad n}} = {- \frac{\frac{1}{{R1} \cdot {R2} \cdot {C1} \cdot {C2}}}{s^{2} + {s \cdot \frac{1}{C1} \cdot \left( {\frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3}} \right)} + \frac{1}{{R2} \cdot {R3} \cdot {C1} \cdot {C2}}}}$

[0021] The characteristic parameters of the circuit of FIG. 1, that isthe gain A0, the cutting frequency ω0 and the merit factor Q, are thefollowing. $\begin{matrix}{A_{0} = {- \frac{R3}{R1}}} \\{\omega_{0} = \sqrt{\frac{1}{{R2} \cdot {R3} \cdot {C1} \cdot {C2}}}} \\{Q = \frac{\sqrt{\frac{C1}{C2}}}{\sqrt{\frac{R2}{R3}} + \sqrt{\frac{R3}{R2}} + \frac{\sqrt{{R2} \cdot {R3}}}{R1}}}\end{matrix}$

[0022] As can be seen, the parameters A0, ω0, and Q depend on the valuesof the components, and by regulating the value of one component, thechange of the three parameters is thus obtained.

[0023] From the above equations the following values R1, R2 and R3 areobtained.${R1} = \frac{1 \pm \sqrt{1 - {4{Q^{2}\left( {1 + {A_{0}}} \right)}\frac{C2}{C1}}}}{2Q\quad \omega \quad {A_{0}}C_{2\quad}}$${R2} = \frac{2Q}{\omega \quad {C_{1}\left( {1 \pm \sqrt{1 - {4{Q^{2}\left( {1 + {A_{0}}} \right)}\frac{C2}{C1}}}} \right)}}$${R3} = \frac{1 \pm \sqrt{1 - {4{Q^{2}\left( {1 + {A_{0}}} \right)}\frac{C2}{C1}}}}{2Q\quad \omega \quad {C2}}$

[0024] We refer now to FIG. 2 that represents a system 20 for thedetermination of the component technological distribution.

[0025] A voltage Vref is applied to a terminal of a resistance array Raand to a controlled switch IN1 connected to a controlled switch IN2 andto a capacitor Cc. The capacitor Cc is connected in turn to a controlledswitch IN3 and to a controlled switch IN4. The switches IN2 and IN3 areconnected to the non-inverting input of an operational OP2, to thenon-inverting input of an operational OP3 and to a voltage Vdd/2.

[0026] The switch IN4 is connected to the inverting input of theoperational OP2, to a controlled switch IN6, to a controlled switch IN5and to a capacitor Cf. The controlled switch IN6, in parallel to thecapacitor Cf, is connected to the output of the operational OP2 and tothe inverting input of the operational OP3. The switch IN5 is connectedto the other terminal of the resistance array Ra.

[0027] The switches IN2, IN4 and IN5 are controlled by a square wavesignal ck1. The switches IN1, IN3 and IN6 are controlled by a squarewave signal ck2.

[0028] The output of the operational OP3 is applied to the input of anup-down counter Cont at four bits, having a synchronism signal ck. Itprovides the output signals I1-I4, applied to the resistance array Ra.

[0029] The resistance array Ra is shown in FIG. 3. It is preferablycomposed of five resistances Roff, δR, 2δR, 4δR, 8δR, placed in series,and four switches respectively controlled by signals I1-I4, that connector disconnects the resistances δR, 2δR, 4δR, 8δR from the resistancearray Ra.

[0030] Referring to FIG. 2, the charge quantity injected by the switchedcapacitor Cc is proportional to the reference voltage Vref, while thecurrent flowing in the array Ra, besides depending on Vref, also dependson the resistance value of Ra. From the difference of these signals, thesignal error is obtained, integrated by the capacitor Cf placed asfeedback to the operational OP2. Then at the circuit output, since ininput there is a constant voltage, there results a voltage ramp.

[0031] Having chosen the value of the reference voltage Vref and thecapacitor Cf, the slope of the voltage ramp depends only on the arrayRa.

[0032] The output Vo is compared with the voltage Vdd/2, through acomparator (the operational OP3), so as to have the variation sign to beset to the array Ra, in order to guarantee equality with the referencevoltage Vref. The sign (represented by a 0 or a 1) controls an N-bitUP-DOWN counter Cont, where N is the number of resistances thatconstitute the array Ra. In presence of a 1 the calculation is increasedby increasing its value; with a 0 the back calculation is determined bydecreasing its value. The switch IN6 in parallel with the operationalOP3 is used to periodically discharge (with ck2) the present charge onCf in order to be able to integrate only that one effectively injected.The system 20 is timed with two synchronism signals ck1 and ck2, onecomplementary to the other but of a small hysteresis.

[0033] In this way it is possible to tie the possible combinations atthe output of the counter Cont to a corresponding number of levels ofthe technological distribution of the component values.

[0034] The array Ra is controlled by the counter Cont so as to introducean overall resistance as close as possible to the nominal one chosen,keeping in mind that the resistances composing it also have the samedegree of standard deviation. The resistances of Ra, therefore, willhave to introduce resistance values as to be able to recompose thenominal value in each case.

[0035] The array Ra is structured with a series of five resistances ofwhich four can be short-circuited by the counter. The resistance Roffavoids the short circuit when the outputs of the counter are all low. Toperform the sizing it is enough to know the value of Roff and δR; infact, the other resistances are multiples of the first one.

[0036] The value of the array Ra is given by the following formula.

R _(a)=(I+ε)·(R _(off) +nδR)

[0037] Where ε represents the standard deviation of the technologicaldistribution of the components and n the decimal equivalent of thecalculation of the counter Cont.

[0038] Then, one considers the following expressions.

R _(off)(1−ε)<R _(nom)

(R _(off)+15δR)(1−ε)>R _(nom)

R _(off)(1+ε)<R _(nom)

(R _(off)+15δR)(1+ε)>R _(nom)

[0039] Where Rnom is the required (nominal) resistance value.

[0040] Resolving these expressions obtains the following.$\begin{matrix}{R_{off} < \frac{R_{nom}}{1 + ɛ}} \\{{\delta \quad R} > {{\frac{1}{15} \cdot \left( \frac{R_{nom}}{1 - ɛ} \right)} - R_{off}}}\end{matrix}$

[0041] We now consider FIG. 4, which is a block diagram of a controlsystem for the characteristic parameters of an active filter accordingto an embodiment of the present invention. It shows a system 20 (FIG. 2)for the determination of the technological distribution of thecomponents that provides a digital signal Ein at n bits to anelaboration system 40, that provides three digital signals E1, E2 and E3each at n bits to a biquadratic cell 10 with only one operationalamplifier OP1 like that of FIG. 1. The biquadratic cell 10, in thisembodiment replacing the resistances R1, R2, and R3, has threeresistance arrays Ra of the type of that of FIG. 3 controlled by thethree digital signals E1, E2 and E3.

[0042] From the information of the signal Ein, the elaboration system 40determines the digital values of the signals E1, E2 and E3 that willdetermine the correct value of the resistances R1, R2 and R3, toeliminate the error due to the technology distribution and to plan thevalue of the desired parameters A0, ω0, Q.

[0043] According to the Ein value (and that is n) and to that of thearray Ra, through the following formula

R _(a)=(1+ε)·(R _(off) +nδR)

[0044] the value of the standard deviation ε of the technologicaldistribution of the components can be determined.

[0045] The values of R1, R2 and of R3 are determined through theabove-mentioned formulas, they are corrected in order to take intoaccount the standard deviation ε, and the values R1 c, R2 c and R3 c aredetermined, through the following formula $R_{nc} = \frac{R_{n}}{1 + ɛ}$

[0046] where Rnc is the corrected resistance n and Rn the resistance nto be corrected.

[0047] The just-calculated values are those that we have to be able toreconstruct, considering that the resistances, effectively realized onthe silicon, are really different of an amount equal to ε. So it isworthwhile to look for a resistive value that, varied according to thedistribution, gives us the above-mentioned resistances.

[0048] For each resistance, the value which E1, E2 and E3 should assumeare able to effect the resistance in question with the elements of thearrays. The knowledge of such signals allows us to realize a resistanceof the wanted value.

[0049] Being aware of the nominal values of the resistances that composethe arrays Ra of the resistances R1, R2 and R3, by varying thepossibilities offered by the signals E1, E2 and E3, a digital word ischosen for every resistance that closes the appropriate switches so asto produce the desired resistance.

[0050] By an array Ra formed by a fixed resistance and four resistancescontrollably connectable it is possible to choose a resistance among the16 possible.

[0051] In other words the nominal value of the resistances Rnc,previously calculated, with the value obtainable by applying thedifferent digital words (E1-E3) is compared with the arrays Ra, thatrepresent the resistances R1-R3, and the nearest value (at minimumdistance) to the wanted nominal value is chosen.

[0052] It is possible to apply this method also to passive circuitalelements of a different type (for instance, capacitors), or to maintainfixed a passive element and to program, according to an embodiment ofthe present invention, the other two passive elements.

[0053] The filter 10 may be disposed on an integrated circuit, which onemay incorporate into an electronic system.

What is claimed is:
 1. Control system for the characteristic parametersof an active filter comprising: a system for the determination oftechnological distribution of the components that provides theinformation related to said technological distribution of thecomponents; an elaboration system for said information related to saidtechnological distribution of the components; an active filter includingat least two programmable passive circuital elements receiving saidinformation related to said technological distribution of thecomponents; said elaboration system, being aware of the topology of saidactive filter, comprises means for determining the value of said atleast two programmable passive circuital elements; means for correctingthe value of said at least two programmable passive circuital elementsaccording to the value of the information related to said technologicaldistribution of the components; means for determining the programmingvalues of said at least two programmable passive circuital elements. 2.Control system according to claim 1 wherein said active filter isconstituted by a biquadratic cell with only one operational amplifier.3. Control method of the characteristic parameters of an active filtercomprising: a system for the determination of the technologicaldistribution of the components that provides the information related tosaid technological distribution of the components; an elaboration systemfor said information related to said technological distribution of thecomponents; an active filter including at least two programmable passivecircuital elements receiving said information related to saidtechnological distribution of the components; said elaboration system,being aware the topology of said active filter, determines the value ofsaid at least two programmable passive circuital elements; corrects thevalue of said at least two programmable passive circuital elementsaccording to the value of the information related to said technologicaldistribution of the components; determines the programming values ofsaid at least two programmable passive circuital elements.
 4. Controlmethod according to claim 3 wherein said active filter is constitutedonly of a biquadratic cell with an operational amplifier.
 5. Controlmethod according to claim 4 wherein said system for the determination ofthe technological distribution of the components determines thedistribution by the following formula: R _(a)=(1+ε)·(R _(off) +nδR) 6.Control method according to claim 4 wherein said elaboration systemdetermines the value of said at least two programmable passive circuitalelements by the following formulas: $\begin{matrix}{{R1} = \frac{1 \pm \sqrt{1 - {4{Q^{2}\left( {1 + {A_{0}}} \right)}\frac{C2}{C1}}}}{2Q\quad \omega {A_{0}}C_{2}}} \\{{R2} = \frac{2Q}{\quad {\omega \quad {C_{1}\left( {1 \pm \sqrt{1 - {4{Q^{2}\left( {1 + {A_{0}}} \right)}\frac{C2}{C1}}}} \right)}}}} \\{{R3} = \frac{1 \pm \sqrt{1 - {4{Q^{2}\left( {1 + {A_{0}}} \right)}\frac{C2}{C1}}}}{2Q\quad \omega \quad {C2}}}\end{matrix}$


7. Control method according to claim 4 wherein said elaboration systemcorrects the value of said at least two programmable passive circuitalelements according to the following formula:$R_{nc} = \frac{R_{n}}{1 + ɛ}$


8. A method, comprising: determining an amount by which a first actualvalue of a first electronic component deviates from an expected value;and adjusting a second electronic component from an initial value towarda desired value based on the determined amount.
 9. The method of claim 8wherein: determining the amount comprises setting the amount equal tothe quotient of the first actual value divided by the expected value;and adjusting the second electronic component comprises adjusting thesecond electronic component closer to a quotient of the initial valuedivided by the amount.
 10. The method of claim 8 wherein determining theamount comprises: driving the first electronic component with an inputsignal; adjusting the value of the first electronic component until anoutput signal has a desired value; determining the first actual valuebased on the input and output signals when the output signal has thedesired value; and determining the expected value of the firstelectronic component based on an amount by which the value of the firstelectronic component is adjusted.
 11. An electronic system, comprising:a first circuit including a first electronic component having an initialvalue; and a second circuit including a second electronic component andoperable to determine an amount by which an actual value of the secondelectronic component deviates from an expected value and to adjust thefirst electronic component from the initial value toward a desired valuebased on the determined amount.
 12. The electronic system of claim 11wherein the first and second electronic components respectively comprisefirst and second resistors.
 13. The electronic system of claim 11wherein the first circuit comprises a filter.
 14. The electronic systemof claim 11, further comprising an integrated circuit on which the firstand second circuits are disposed.
 15. The electronic system of claim 11wherein the second circuit is operable to determine the amount by:driving the second electronic component with an input signal to generatean output signal; adjusting the value of the second electronic componentuntil the output signal has a desired value; determining the actualvalue of the second electronic component based on the input and outputsignals when the output signal has the desired value; and determiningthe expected value of the second electronic component based on a valuesetting of the second component.
 16. The electronic system of claim 15wherein adjusting the value of the second electronic component comprisesadjusting the value setting of the second component.